Abstract
We describe the solution to a mathematical question that arises in the context of constructing four-couple dances in which there is no repetition in the positions and partnerships formed by the dancers during the intermediate stages of the dance. Our description makes use of various properties of permutations and cycle notation which are well known to mathematicians but probably less so more broadly. An implementation of the mathematical solution as an actual dance is discussed. We also consider generalizations of the original problem and explain a connection with the theory of orthogonal Latin squares.
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